These systems are famous for marginal performance at idle in hot weather, especially an '89 (which I have and get similar results). Even with the aux fan and clutched main fan, you are probably getting enough air flow to keep the engine temp within an acceptable range. If you raise the rpm's whilst at idle, you will notice a difference. Get yourself a small thermometer for AC work (AutoZone) and pop it into the center duct and check the temps at idle and at 2000 rpm. If your cooldown time is excessive, but it ultimately gets "cold", I'd be willing to bet you have lost some R-12 and will need a top up. Have it checked as advised, make sure fans are working and don't ever just sit in traffic.

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Jeff Lawrence
1989 300e
2000 Dodge Grand Caravan SE
No matter what you fix, there will always be something else to fix..
"Warranty" is just another way of postponing the inevitable.